What is the integral of (ln(7x))^2 ?

The integral of (ln(7x))^2 is xln^2(7x)-2(xln(7x)-x)+C

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integral of (ln(7x))^2

\int (ln (7 x))^{2} d x

x ln^{2} (7 x) - 2 (x ln (7 x) - x) + C

Solution steps

\int (ln (7 x))^{2} d x

Apply Integration By Parts

: x ln^{2} (7 x) - \int 2 ln (7 x) d x

= x ln^{2} (7 x) - \int 2 ln (7 x) d x

\int 2 ln (7 x) d x = 2 (x ln (7 x) - x)

= x ln^{2} (7 x) - 2 (x ln (7 x) - x)

Add a constant to the solution

= x ln^{2} (7 x) - 2 (x ln (7 x) - x) + C

\int_{0}^{x^{2}} e^{t^{2}} d t

t \to 2 lim (\frac{t + 2}{t ^{2} - 4})

x \to \infty lim (- 2 x - 1)

f (x) = \frac{2}{x - 8}, at x = 10

\int 22 sec^{4} (θ) tan^{2} (θ) d θ

What is the integral of (ln(7x))^2 ?
The integral of (ln(7x))^2 is xln^2(7x)-2(xln(7x)-x)+C